fix(search): use shared inline tool activity #32858

Job	Run time
Test and Build / Lint and Test	3m 16s
Test and Build / PostgreSQL integration (push)	7m 31s
Test and Build / PostgreSQL integration (migrate)	6m 16s
Test and Build / Build App	4m 44s
Test and Build / Test (shard 3)	3m 3s
Test and Build / Test (shard 2)	2m 36s
Build Dev ECR	0s
Build ARM64 (GHCR Only)	0s
Prepare Trigger.dev	0s
Build AMD64	0s
Check Desktop Signing Secrets	0s
Create Desktop Prerelease	0s
Desktop Prerelease Build	0s
Publish Desktop Prerelease	-1s
Prune Desktop Prereleases	-1s
Detect Version	-5s
Check Docs Changes	-8s
Detect Desktop Changes	-8s
Migrate Dev DB	-10s
Migrate DB	0s
Promote Images	0s
Promote Trigger.dev	0s
Process Docs	0s
Create GHCR Manifests	0s
Resolve Attestation Subjects	-1s
Attest Images	-1s
Create GitHub Release	-1s
Desktop Release	-1s
	26m 49s

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